I own a top loading Frigidaire Washing Machine (model #FWX970EW1) and it stopped agitating today.

1. When you start a cycle, it will fill with water.

2. During the wash cycle, the motor is humming but the drum is not agitating. :confused:

3. If you advance the controls to the rinse/spin cycle, the washer will drain the water and the drum will spin.

What could be wrong?

What steps should I use to isolate the problem?

The same motor - but different windings - is used to rotate and spin.
You say that the motor allows spinning, so nothing is blocked.
It therefore seems most probable that the capacitor for the motor rotate windings has shorted, causing the motor not to run during rotation cycles.
Replace that (or both) capacitors. Not very expensive items available form every same-brand washing machine dealer.
Alternative : please read the service manual instructions and/or order the spareparts, available from Sears.
(The Sears website - Service) (http://www.searspartsdirect.com/partsdirect/index.action?sid=PSHx20080114x00001)

Success !